$\begin{array} { l }r=\frac{ 30 }{ 60 },\\r=\frac{ 15 }{ 30 },\\r=\frac{ \frac{ 15 }{ 2 } }{ 15 }\end{array}$
Cancel out the common factor $30$$\begin{array} { l }r=\frac{ 1 }{ 2 },\\r=\frac{ 15 }{ 30 },\\r=\frac{ \frac{ 15 }{ 2 } }{ 15 }\end{array}$
Cancel out the common factor $15$$\begin{array} { l }r=\frac{ 1 }{ 2 },\\r=\frac{ 1 }{ 2 },\\r=\frac{ \frac{ 15 }{ 2 } }{ 15 }\end{array}$
Simplify the complex fraction$\begin{array} { l }r=\frac{ 1 }{ 2 },\\r=\frac{ 1 }{ 2 },\\r=\frac{ 1 }{ 2 }\end{array}$
Since the ratio between each pair of consecutive terms is the same, the sequence is geometric and the common ratio is $r=\frac{ 1 }{ 2 }$$r=\frac{ 1 }{ 2 }$
Substitute $\frac{ 1 }{ 2 }$ for $r$ in the recursive equation for a geometric sequence, $a_n=ra_n-1$$a_n=\frac{ 1 }{ 2 }a_n-1$
The recursive formula consists of the first term and the recursive equation$\begin{array} { l }a_1=60,& a_n=\frac{ 1 }{ 2 }a_n-1\end{array}$